Building blocks of etale endomorphisms of complex projective manifolds

TL;DR

This paper classifies etale endomorphisms of complex projective manifolds into fundamental types, assuming the good minimal model conjecture, highlighting their construction from abelian varieties and weak Calabi-Yau varieties.

Contribution

It provides a classification of etale endomorphisms based on two main building blocks under a major conjecture, advancing understanding of their structure.

Findings

Endomorphisms are constructed from abelian varieties and weak Calabi-Yau varieties.

Classification holds assuming the good minimal model conjecture.

Clarifies the structure of etale endomorphisms in complex geometry.

Abstract

Etale endomorphisms of complex projective manifolds are constructed from two building blocks up to isomorphism if the good minimal model conjecture is true. They are the endomorphisms of abelian varieties and the nearly etale rational endomorphisms of weak Calabi-Yau varieties.